Self-study helps students to build confidence in learning. It boosts the self-esteem of the learners. Recent surveys suggested that close to 50% learners were self-taught using internet resources and upskilled themselves. A student may spend 1 hour to 6 hours in a day in upskilling self. The probability distribution of the number of hours spent by a student is given below : P(X = x) = { kx^2, for x = 1, 2, 3; 2kx, for x = 4, 5, 6; 0, otherwise where x denotes the number of hours. Based on the above information, answer the following questions : (i) Express the probability distribution given above in the form of a probability distribution table. (ii) Find the value of k. (iii) (a) Find the mean number of hours spent by the student. OR (iii) (b) Find P(1 < X < 6).